Question

7) Suppose you wish to test if a number cube (die) is loaded or not. If the die is not loaded, the theoretical probabilities for each roll should be:

1- 16 2/3%

2- 16 2/3%

3- 16 2/3%

4- 16 2/3%

5- 16 2/3%

6- 16 2/3%

You roll the die 87 times and come up with the following distribution:

1- 14

2- 11

3- 21

4- 13

5- 15

6- 13

What type of test should be used in this situation and what is the test statistic?

a) χ² Goodness of Fit; χ² = 4.103

b) Two proportion z test; z = 0.249

c) One proportion z test; z = 1.140

d) χ² Goodness of Fit; χ² = 4.074

e) One proportion z test; z = 0.249

Answer 1

We are doing here the goodness of fit test which is a chi square test.

The expected frequency for each outcome here is computed as:
= Total number of times the dice is rolled / 6

= 87/6

The chi square test statistic here is computed as:

X	O_i	E_i	(O_i - E_i)^2/E_i
1	14	14.5	0.017241379
2	11	14.5	0.844827586
3	21	14.5	2.913793103
4	13	14.5	0.155172414
5	15	14.5	0.017241379
6	13	14.5	0.155172414
	87	87	4.103448276

Therefore 4.103 is the required test statistic value here. a) is the correct answer here.